Fiber waste generated during operation of a circular knitting machine tends to accumulate in the machine's knitting section yarn carrier, sinker, sinker cap and/or needle selector components. The fiber waste may then be knit into fabric being knitted by the machine. When this occurs, it is likely to cause damage to the fabric and also to the knitting needles of the machine. In order to reduce the possibility of such damage occurring, circular knitting machines have heretofore been provided with a plurality of air ejection pipes that are adapted to blow fiber waste off of specific parts of the machine's knitting section while undergoing rotation in a direction that is the same as or opposite to the direction of rotation of the needle cylinder of the machine. However, since the outlet opening at the tip of each air ejection pipe can direct air in only a single direction, the amount of fiber waste that can be removed by each pipe is limited. Japanese Patent publication No. Hei 1-38899 discloses a proposed improvement wherein the outlet end of an air ejection pipe is provided with an elastic nozzle that undergoes wobbling motion. Although the air discharged from the air ejection pipes with the wobbling nozzles contacts some additional areas and effectively remove fiber waste from them, it has heretofore failed to reach fiber waste generated by engagement of stitches with each other as the stitches clear the knitting needles of the machine. The fiber waste which the air fails to remove tends to enter the needle grooves of the needle cylinder and to adhere thereto due to the presence of oil in such grooves. This of course made it quite difficult to remove the fiber waste.